Advanced numerical simulation of heat transfer problems

Owing to recent advances in computer hardware, numerical analysis is now widely used in various kinds of design of manufacturing products and of investigation of complex phenomena. The substantial subjects for practical use of numerical analysis are a development of numerical simulation system accompanied by a fully automatic mesh generation system based on CAD data and a highly efficient numerical technique for very large-scale analysis. Two approaches may be the candidates along this line. One is the finite element analysis using tetrahedral elements and the other is the Voxel method using uniform orthogonal grids. These two approaches are investigated for practical large-scale analysis on heat transfer and fluid flow problems. Firstly, a parallel large eddy simulation for viscous incompressible flow with heat transfer based on the finite element method using tetrahedral elements is presented. A new algorithm based on the SIMPLER method is proposed to solve Navier-Stokes equations, in which balancing tensor diffusivity is introduced to ensure numerical stability. The Smagorinsky model is applied to approximate the Reynolds stress and the zero-equation model is applied to solve energy equation. Parallelization of the code is based on the domain decomposition method and the recursive graph bisection algorithm is used to reduce the communication time between processors. Numerical results for heat transfer problems in a rotating cavity show good agreement with experimental results. Secondly, a two-dimensional simulation of fluidized beds based on the Voxel method combined with the discrete element method (DEM), in which particle motion is calculated using ordinary Newton's equation of motion, modeling the contact forces by the DEM. The local averaged equations are solved to analyze the fluid motion, taking the interaction between fluid and particle into consideration. Flow and temperature fields are solved by the finite difference method with uniform grid size, the so-called Voxel method. Numerical results for a fluidized bed agree well with experimental results. The extension of this method to these-dimensional problem is straightforward and seems to be promising for the practical large-scale heat transfer problems. Through these two kinds of analyses, both the finite element method using tetrahedral elements and the Voxel method using orthogonal uniform grids have proved to be a powerful tool for practical large-scale heat transfer and fluid flow problems. Refs. 1 (author)